Theorems · Theorem · measure theory
MeasureTheory.withDensity_eq_zero_iff
∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f : α → ENNReal},
AEMeasurable f μ → (μ.withDensity f = 0 ↔ f =ᵐ[μ] 0)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- MeasureTheory.aestatement and proof · cited by 2,352
- Filter.EventuallyEqstatement and proof · cited by 1,912
- MeasureTheory.lintegralproof · cited by 1,152
- AEMeasurablestatement and proof · cited by 840
- MeasureTheory.Measure.withDensitystatement · cited by 265
- MeasurableSet.univproof · cited by 178
- MeasureTheory.Measure.restrict_univproof · cited by 76
- MeasureTheory.withDensity_applyproof · cited by 73
- MeasureTheory.Measure.measure_univ_eq_zeroproof · cited by 26
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.rnDeriv_eq_zeroproof · cited by 6
- MeasureTheory.withDensity_eq_zeroproof · cited by 0